Yohannes Ketema

Vibration damping through the use of materials with memory

We study the dynamics of a lumped mass linear oscillator that is damped through the use of a material with memory in which the internal dissipative forces depend not only on current but also on previous deformations. This effective memory is governed by two parameters: the relaxation modulus G0, and relaxation time γ, which also govern the vibration-damping properties of the material. Conditions for optimal damping in the unforced case corresponding to critical damping of a linear oscillator with viscous damping are derived, and the response of the oscillator in the case of sinusoidal excitation is studied. When the relaxation time is small the history type damping is modeled approximately by the action of a classical viscous damper with small viscosity. However, when the relaxation time is sufficiently large, this damping mechanism adds to the system a new higher resonance frequency that depends on G0 and γ. Since the oscillator is active over a wide range of frequencies, it has potential applications to the development of adaptive damping devices.

A thermoviscoelastic dynamic vibration absorber

A dynamic vibration absorber with a viscoelastic element is studied. The viscoelastic element is modeled as a material with memory in which the internal dissipative force depends on current, as well as previous deformations. The viscoelastic behavior is governed by two parameters: the relaxation modulus G 0 , and the relaxation time γ. We apply the principle of time-temperature superposition to affect a dependence of the relaxation time γ on temperature. This temperature dependence can be used to tune a vibration absorber so as to be effective at more than one excitation frequency.

Controllability and Reachability for Micro-Aerial-Vehicle Trajectory Planning in Winds

CD0 = zero-lift drag coefficient CL, CD = lift and drag coefficients D = aerodynamic drag Emax = maximum lift-to-drag ratio or aerodynamic efficiency g = gravitational acceleration I = performance index K = induced drag factor L = aerodynamic lift m = aircraft mass N = number of nodes in the discretization of time interval n = load factor S = vehicle reference area T = engine thrust t = time V = airspeed VI = inertial speed Vm = maximum airspeed trajectory constraint Vmax = maximum permitted airspeed for vehicle Wm = wind magnitude Wx,Wy = east and north wind components x, y = east and north positions = bank angle m = maximum bank angle trajectory constraint = direction angle measured clockwise from the North = air density = normalized time = heading angle measured clockwise from the North I = inertial heading angle measured clockwise from the North w = wind direction angle measured clockwise from the North 0 = derivative with respect to normalized time

Micro Air Vehicle Trajectory Planning in Winds

M ICRO aerial vehicles (MAVs) are small aerial vehicles, generallywith dimensions on the order of 1 ft (or 0.3m). Their small sizes often imply that their flight speeds are also small, roughly on the order of 20–60 km=h. MAVs come in a wide variety of forms, such as fixed wing, flapping wing, and rotary wing [1]. They are finding increasingly more applications in such areas as military missions, reconnaissance of hazardous or remote areas, and monitoring of indoor areas. Because of their small sizes and light weights, MAV flight trajectories are significantly susceptible to winds in general. For example, it is possible for the wind to be so strong that the MAV is unable to advance in certain directions. (This problem can be formulated in terms of the controllability of a point and its associated reachable set, see [2].) It is therefore necessary to develop a systematic approach toMAV trajectory generation that addresses the characteristic issues of MAV flights in winds. Specifically, the following three points must be considered: 1) Target points may not always be feasible due to winds. 2) Wind profiles may have significant effects on fuel costs (both desirable and undesirable). 3) Trajectory generation must always yield a feasible solution due to the absence of human operators. The main goal of this note is to study meaningful trajectory generation problem formulations for MAV trajectories in winds, to address all three of the issues discussed above that characterize MAV flights. Specifically, MAV flights in winds are formulated as nonlinear optimal control problems, with proper constraints on states and controls. In particular, the reaching of a target point is enforced via a penalty term in the performance index. Thus, while a target point is not necessarily reached, a flyable trajectory that is optimal under prevailing conditions is obtained. Both constant and position dependent wind is considered.

Optimal Satellite Transfers Using Relative Motion Dynamics

A first-order approximation of optimal two-burn transfers between satellite orbits within a formation is presented and discussed. The orbital transfer problem is based on the well-known fact that, to first order, such orbits are elliptic, with centers at the target or offset in the in-track direction. The methodology allows for a target in a (generally) elliptic orbit in its motion about the center of force. The solution obtained makes use of a transformation of the problem to the reference frame of an auxiliary target in circular orbit in the inertial frame. The total required |Δ v| is expressed in terms of the identifying parameters for the initial and final orbits in the formation, corresponding to their respective sizes as measured by their minor axes, location of their centers, and their orientation. This expression allows for numerical parametric studies in the case where the initial and final orbits are in the same or parallel planes. It is shown that the optimal total |Δ v| depends on the relative sizes of the orbits and the distance between their centers. When the initial and final orbits are concentric, four optimal two-burn transfers, all of the same total |Δ v|, are identified. It is further shown that the optimal |Δ v| changes with the distance between the centers of the orbits and attains a minimum when this distance is about 2.2 times the difference between the minor axes of the orbits.

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

A non-linear oscillator with history dependent force

Abstract We study the dynamics of a non-linear damped one-degree-of-freedom oscillator whose response force is dependent on the history of the motion and is of the relaxing type. Such an oscillator may serve as a simple model for mechanical applications where viscoelastic materials are used for the purpose of vibration damping and/or isolation. In the simplest cases history dependent forces are characterized by two parameters: the relaxation modulus Φ0 and the relaxation time γ. Through the use of a version of Melnikovs method we show how the two parameters govern the existence of non-linear subharmonic orbits. We suggest an experimental method for determining both parameters.

Formation stability with limited information exchange between vehicles

We study the role of information flow, and especially the rate of update of information among the vehicles in a formation, on the stability of the formation. The problem is initially posed in the general nonlinear context and a linear special case is studied in detail. We present numerical examples that illustrate the results. We also study briefly the effect of imprecise communications on the stability of a formation.

Travel trajectory planning for Micro air vehicles in winds

Micro aerial vehicles (MAVs) are designed to fly at speeds that are comparable to those of typical winds. As a result, trajectory planning for MAVs must incorporate wind as a significant factor that may affect both feasibility and optimality. In particular, unlike conventional trajectory generation, where an aircraft can always be assumed to be able to fly against the wind, MAV trajectory generation may have to deal with target points that are infeasible due to wind, at least for given time intervals. In these cases, it is important that a trajectory generation algorithm returns the best alternative trajectory that the MAV should follow, for example until a feasible trajectory to the target is available. This paper is concerned with studying problem formulations for optimal trajectory generation for MAVs in winds, that always results in feasible trajectories despite prevailing wind characteristics. In addition we investigate how regional wind patterns affect the design of optimal MAV trajectories. The results are especially applicable for automatic trajectory generation algorithms where human decision-making is not practical. Nomenclature

Stability of formations with delays in information exchange.

The effect of delays in information exchange on the stability of a formation is studied. Upper limits for allowable delays are obtained through the use of two methods applicable to a class of systems.